J. Yang, J. Leconte, E. T. Wolf, T. Merlis, D. D. B. Koll, F. Forget, and D. S. Abbot. Simulations of Water Vapor and Clouds on Rapidly Rotating and Tidally Locked Planets: A 3D Model Intercomparison. Astrophysical Journal, 875:46, 2019. [ bib | DOI | PDF version | ADS link ]
Robustly modeling the inner edge of the habitable zone is essential for determining the most promising potentially habitable exoplanets for atmospheric characterization. Global climate models (GCMs) have become the standard tool for calculating this boundary, but divergent results have emerged among the various GCMs. In this study, we perform an intercomparison of standard GCMs used in the field on a rapidly rotating planet receiving a G-star spectral energy distribution and on a tidally locked planet receiving an M-star spectral energy distribution. Experiments both with and without clouds are examined. We find relatively small difference (within 8 K) in global-mean surface temperature simulation among the models in the G-star case with clouds. In contrast, the global-mean surface temperature simulation in the M-star case is highly divergent (2030 K). Moreover, even differences in the simulated surface temperature when clouds are turned off are significant. These differences are caused by differences in cloud simulation and/or radiative transfer, as well as complex interactions between atmospheric dynamics and these two processes. For example we find that an increase in atmospheric absorption of shortwave radiation can lead to higher relative humidity at high altitudes globally and, therefore, a significant decrease in planetary radiation emitted to space. This study emphasizes the importance of basing conclusions about planetary climate on simulations from a variety of GCMs and motivates the eventual comparison of GCM results with terrestrial exoplanet observations to improve their performance.
P. Auclair-Desrotour, J. Leconte, and C. Mergny. Generic frequency dependence for the atmospheric tidal torque of terrestrial planets. Astronomy Astrophysics, 624:A17, 2019. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. Thermal atmospheric tides have a strong impact on the rotation of terrestrial planets. They can lock these planets into an asynchronous rotation state of equilibrium. <BR /> Aims: We aim to characterize the dependence of the tidal torque resulting from the semidiurnal thermal tide on the tidal frequency, the planet orbital radius, and the atmospheric surface pressure. <BR /> Methods: The tidal torque was computed from full 3D simulations of the atmospheric climate and mean flows using a generic version of the LMDZ general circulation model in the case of a nitrogen-dominated atmosphere. Numerical results are discussed with the help of an updated linear analytical framework. Power scaling laws governing the evolution of the torque with the planet orbital radius and surface pressure are derived. <BR /> Results: The tidal torque exhibits (i) a thermal peak in the vicinity of synchronization, (ii) a resonant peak associated with the excitation of the Lamb mode in the high frequency range, and (iii) well defined frequency slopes outside these resonances. These features are well explained by our linear theory. Whatever the star-planet distance and surface pressure, the torque frequency spectrum - when rescaled with the relevant power laws - always presents the same behaviour. This allows us to provide a single and easily usable empirical formula describing the atmospheric tidal torque over the whole parameter space. With such a formula, the effect of the atmospheric tidal torque can be implemented in evolutionary models of the rotational dynamics of a planet in a computationally efficient, and yet relatively accurate way.
P. Auclair-Desrotour, S. Mathis, J. Laskar, and J. Leconte. Oceanic tides from Earth-like to ocean planets. Astronomy Astrophysics, 615:A23, 2018. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, two-dimensional (2D) models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional (3D) effects related to the ocean's vertical structure. <BR /> Aims: Our goal is to investigate, in a consistant way, the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modelling that allows one to treat a wide range of cases from shallow to deep oceans. <BR /> Methods: A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification, and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification. <BR /> Results: In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt-Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response becomes 3D. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to significantly affect the evolution time scale of the planetary rotation.
P. Auclair-Desrotour and J. Leconte. Semidiurnal thermal tides in asynchronously rotating hot Jupiters. Astronomy Astrophysics, 613:A45, 2018. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. Thermal tides can torque the atmosphere of hot Jupiters into asynchronous rotation, while these planets are usually assumed to be locked into spin-orbit synchronization with their host star. <BR /> Aims: In this work, our goal is to characterize the tidal response of a rotating hot Jupiter to the tidal semidiurnal thermal forcing of its host star by identifying the structure of tidal waves responsible for variation of mass distribution, their dependence on the tidal frequency, and their ability to generate strong zonal flows. <BR /> Methods: We develop an ab initio global modelling that generalizes the early approach of Arras Socrates (2010, ApJ, 714, 1) to rotating and non-adiabatic planets. We analytically derive the torque exerted on the body and the associated timescales of evolution, as well as the equilibrium tidal response of the atmosphere in the zero-frequency limit. Finally, we numerically integrate the equations of thermal tides for three cases, including dissipation and rotation step by step. <BR /> Results: The resonances associated with tidally generated gravito-inertial waves significantly amplify the resulting tidal torque in the range 1-30 days. This torque can globally drive the atmosphere into asynchronous rotation, as its sign depends on the tidal frequency. The resonant behaviour of the tidal response is enhanced by rotation, which couples the forcing to several Hough modes in the general case, while the radiative cooling tends to regularize it and diminish its amplitude.
J. Leconte. Continuous reorientation of synchronous terrestrial planets due to mantle convection. Nature Geoscience, 11:168-172, 2018. [ bib | DOI | arXiv | PDF version | ADS link ]
Many known rocky exoplanets are thought to have been spun down by tidal interactions to a state of synchronous rotation, in which a planet's period of rotation is equal to that of its orbit around its host star. Investigations into atmospheric and surface processes occurring on such exoplanets thus commonly assume that day and night sides are fixed with respect to the surface over geological timescales. Here we use an analytical model to show that true polar wanderwhere a planetary body's spin axis shifts relative to its surface because of changes in mass distributioncan continuously reorient a synchronous rocky exoplanet. As occurs on Earth, we find that even weak mantle convection in a rocky exoplanet can produce density heterogeneities within the mantle sufficient to reorient the planet. Moreover, we show that this reorientation is made very efficient by the slower rotation rate of a synchronous planet when compared with Earth, which limits the stabilizing effect of rotational and tidal deformations. Furthermore, a relatively weak lithosphere limits its ability to support remnant loads and stabilize against reorientation. Although uncertainties exist regarding the mantle and lithospheric evolution of these worlds, we suggest that the axes of smallest and largest moment of inertia of synchronous exoplanets with active mantle convection change continuously over time, but remain closely aligned with the star-planet and orbital axes, respectively.
M. Turbet, J. Leconte, F. Selsis, E. Bolmont, F. Forget, I. Ribas, S. N. Raymond, and G. Anglada-Escudé. The habitability of Proxima Centauri b. II. Possible climates and observability. Astronomy Astrophysics, 596:A112, 2016. [ bib | DOI | arXiv | PDF version | ADS link ]
Radial velocity monitoring has found the signature of a Msini = 1.3M⊕ planet located within the habitable zone (HZ) of Proxima Centauri. Despite a hotter past and an active host star, the planet Proxima b could have retained enough volatiles to sustain surface habitability. Here we use a 3D Global Climate Model (GCM) to simulate the atmosphere and water cycle of Proxima b for its two likely rotation modes (1:1 and 3:2 spin-orbit resonances), while varying the unconstrained surface water inventory and atmospheric greenhouse effect. Any low-obliquity, low-eccentricity planet within the HZ of its star should be in one of the climate regimes discussed here. We find that a broad range of atmospheric compositions allow surface liquid water. On a tidally locked planet with sufficient surface water inventory, liquid water is always present, at least in the substellar region. With a non-synchronous rotation, this requires a minimum greenhouse warming ( 10 mbar of CO2 and 1 bar of N2). If the planet is dryer, 0.5 bar or 1.5 bars of CO2 (for asynchronous or synchronous rotation, respectively) suffice to prevent the trapping of any arbitrary, small water inventory into polar or nightside ice caps. We produce reflection and emission spectra and phase curves for the simulated climates. We find that atmospheric characterization will be possible via direct imaging with forthcoming large telescopes. The angular separation of 7λ/D at 1 μm (with the E-ELT) and a contrast of 10-7 will enable high-resolution spectroscopy and the search for molecular signatures, including H2O, O2, and CO2. The observation of thermal phase curves can be attempted with the James Webb Space Telescope, thanks to a contrast of 2 × 10-5 at 10 μm. Proxima b will also be an exceptional target for future IR interferometers. Within a decade it will be possible to image Proxima b and possibly determine whether the surface of this exoplanet is habitable.
T. Fouchet, T. K. Greathouse, A. Spiga, L. N. Fletcher, S. Guerlet, J. Leconte, and G. S. Orton. Stratospheric aftermath of the 2010 Storm on Saturn as observed by the TEXES instrument. I. Temperature structure. Icarus, 277:196-214, 2016. [ bib | DOI | arXiv | PDF version | ADS link ]
We report on spectroscopic observations of Saturn's stratosphere in July 2011 with the Texas Echelon Cross Echelle Spectrograph (TEXES) mounted on the NASA InfraRed Telescope Facility (IRTF). The observations, targeting several lines of the CH4ν4 band and the H2 S(1) quadrupolar line, were designed to determine how Saturn's stratospheric thermal structure was disturbed by the 2010 Great White Spot. A study of Cassini Composite Infrared Spectrometer (CIRS) spectra had already shown the presence of a large stratospheric disturbance centered at a pressure of 2 hPa, nicknamed the beacon B0, and a tail of warm air at lower pressures (Fletcher et al. [2012] Icarus 221, 560-586). Our observations confirm that the beacon B0 vertical structure determined by CIRS, with a maximum temperature of 180 1 K at 2 hPa, is overlain by a temperature decrease up to the 0.2-hPa pressure level. Our retrieved maximum temperature of 180 1 K is colder than that derived by CIRS (200 1 K), a difference that may be quantitatively explained by terrestrial atmospheric smearing. We propose a scenario for the formation of the beacon based on the saturation of gravity waves emitted by the GWS. Our observations also reveal that the tail is a planet-encircling disturbance in Saturn's upper stratosphere, oscillating between 0.2 and 0.02 hPa, showing a distinct wavenumber-2 pattern. We propose that this pattern in the upper stratosphere is either the signature of thermal tides generated by the presence of the warm beacon in the mid-stratosphere, or the signature of Rossby wave activity.
E. Bolmont, A.-S. Libert, J. Leconte, and F. Selsis. Habitability of planets on eccentric orbits: Limits of the mean flux approximation. Astronomy Astrophysics, 591:A106, 2016. [ bib | DOI | arXiv | PDF version | ADS link ]
Unlike the Earth, which has a small orbital eccentricity, some exoplanets discovered in the insolation habitable zone (HZ) have high orbital eccentricities (e.g., up to an eccentricity of ˜0.97 for HD 20782 b). This raises the question of whether these planets have surface conditions favorable to liquid water. In order to assess the habitability of an eccentric planet, the mean flux approximation is often used. It states that a planet on an eccentric orbit is called habitable if it receives on average a flux compatible with the presence of surface liquid water. However, because the planets experience important insolation variations over one orbit and even spend some time outside the HZ for high eccentricities, the question of their habitability might not be as straightforward. We performed a set of simulations using the global climate model LMDZ to explore the limits of the mean flux approximation when varying the luminosity of the host star and the eccentricity of the planet. We computed the climate of tidally locked ocean covered planets with orbital eccentricity from 0 to 0.9 receiving a mean flux equal to Earth's. These planets are found around stars of luminosity ranging from 1 L&sun; to 10-4L&sun;. We use a definition of habitability based on the presence of surface liquid water, and find that most of the planets considered can sustain surface liquid water on the dayside with an ice cap on the nightside. However, for high eccentricity and high luminosity, planets cannot sustain surface liquid water during the whole orbital period. They completely freeze at apoastron and when approaching periastron an ocean appears around the substellar point. We conclude that the higher the eccentricity and the higher the luminosity of the star, the less reliable the mean flux approximation.
E. Bolmont, S. N. Raymond, J. Leconte, F. Hersant, and A. C. M. Correia. Mercury-T: A new code to study tidally evolving multi-planet systems. Applications to Kepler-62. Astronomy Astrophysics, 583:A116, 2015. [ bib | DOI | arXiv | PDF version | ADS link ]
A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the MercuryN-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a standard equilibrium tidal model, the constant time lag model. Besides, the evolution of the radius of several host bodies has been implemented (brown dwarfs, M-dwarfs of mass 0.1 M&sun;, Sun-like stars, Jupiter). We validate the new code by comparing its output for one-planet systems to the secular equations results. We find that this code does respect the conservation of total angular momentum. We applied this new tool to the planetary system Kepler-62. We find that tides influence the stability of the system in some cases. We also show that while the four inner planets of the systems are likely to have slow rotation rates and small obliquities, the fifth planet could have a fast rotation rate and a high obliquity. This means that the two habitable zone planets of this system, Kepler-62e ad f are likely to have very different climate features, and this of course would influence their potential at hosting surface liquid water.The code is only available at the CDS via anonymous ftp to <A href=“http://cdsarc.u-strasbg.fr”>http://cdsarc.u-strasbg.fr</A> (ftp://130.79.128.5) or via <A href=“http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/583/A116”>http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/583/A116</A>
J. Leconte, H. Wu, K. Menou, and N. Murray. Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars. Science, 347:632-635, 2015. [ bib | DOI | arXiv | PDF version | ADS link ]
Planets in the habitable zone of lower-mass stars are often assumed to be in a state of tidally synchronized rotation, which would considerably affect their putative habitability. Although thermal tides cause Venus to rotate retrogradely, simple scaling arguments tend to attribute this peculiarity to the massive Venusian atmosphere. Using a global climate model, we show that even a relatively thin atmosphere can drive terrestrial planets rotation away from synchronicity. We derive a more realistic atmospheric tide model that predicts four asynchronous equilibrium spin states, two being stable, when the amplitude of the thermal tide exceeds a threshold that is met for habitable Earth-like planets with a 1-bar atmosphere around stars more massive than ˜0.5 to 0.7 solar mass. Thus, many recently discovered terrestrial planets could exhibit asynchronous spin-orbit rotation, even with a thin atmosphere.
F. Forget and J. Leconte. Possible climates on terrestrial exoplanets. Philosophical Transactions of the Royal Society of London Series A, 372:20130084-20130084, 2014. [ bib | DOI | arXiv | PDF version | ADS link ]
What kind of environment may exist on terrestrial planets around other stars? In spite of the lack of direct observations, it may not be premature to speculate on exoplanetary climates, for instance to optimize future telescopic observations, or to assess the probability of habitable worlds. To first order, climate primarily depends on 1) The atmospheric composition and the volatile inventory; 2) The incident stellar flux; 3) The tidal evolution of the planetary spin, which can notably lock a planet with a permanent night side. The atmospheric composition and mass depends on complex processes which are difficult to model: origins of volatile, atmospheric escape, geochemistry, photochemistry. We discuss physical constraints which can help us to speculate on the possible type of atmosphere, depending on the planet size, its final distance for its star and the star type. Assuming that the atmosphere is known, the possible climates can be explored using Global Climate Models analogous to the ones developed to simulate the Earth as well as the other telluric atmospheres in the solar system. Our experience with Mars, Titan and Venus suggests that realistic climate simulators can be developed by combining components like a “dynamical core”, a radiative transfer solver, a parametrisation of subgrid-scale turbulence and convection, a thermal ground model, and a volatile phase change code. On this basis, we can aspire to build reliable climate predictors for exoplanets. However, whatever the accuracy of the models, predicting the actual climate regime on a specific planet will remain challenging because climate systems are affected by strong positive destabilizing feedbacks (such as runaway glaciations and runaway greenhouse effect). They can drive planets with very similar forcing and volatile inventory to completely different states.
B. Samuel, J. Leconte, D. Rouan, F. Forget, A. Léger, and J. Schneider. Constraining physics of very hot super-Earths with the James Webb Telescope. The case of CoRot-7b. Astronomy Astrophysics, 563:A103, 2014. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. Transit detection from space using ultra-precise photometry led to the first detection of super-Earths with solid surfaces: CoRot-7b and Kepler-10b. Because they lie only a few stellar radii from their host stars, these two rocky planets are expected to be extremely hot. <BR /> Aims: Assuming that these planets are in a synchronous rotation state and receive strong stellar winds and fluxes, previous studies have suggested that they must be atmosphere-free and that a lava ocean is present on their hot dayside. In this article, we use several dedicated thermal models of the irradiated planet to study how observations with NIRSPEC on the James Webb Space Telescope (JWST) could further confirm and constrain, or reject the atmosphere-free lava ocean planet model for very hot super-Earths. <BR /> Methods: Using CoRoT-7b as a working case, we explore the consequences on the phase-curve of a non tidal-locked rotation, with the presence/absence of an atmosphere, and for different values of the surface albedo. We then simulate future observations of the reflected light and thermal emission from CoRoT-7b with NIRSPEC-JWST and look for detectable signatures, such as time lag, of those peculiarities. We also study the possibility to retrieve the latitudinal surface temperature distribution from the observed SED. <BR /> Results: We demonstrate that we should be able to constrain several parameters after observations of two orbits (42 h) thanks to the broad range of wavelengths accessible with JWST: i) the Bond albedo is retrieved to within 0.03 in most cases. ii) The lag effect allows us to retrieve the rotation period within 3 h of a non phase-locked planet, whose rotation would be half the orbital period; for longer period, the accuracy is reduced. iii) Any spin period shorter than a limit in the range 30-800 h, depending on the thickness of the thermal layer in the soil, would be detected. iv) The presence of a thick gray atmosphere with a pressure of one bar, and a specific opacity higher than 10-5 m-2 kg-1 is detectable. v) With spectra up to 4.5 μm, the latitudinal temperature profile can be retrieved to within 30 K with a risk of a totally wrong solution in 5% of the cases. This last result is obtained for a signal-to-noise ratio around 5 per resel, which should be reached on Corot-7 after a total exposure time of ˜70 h with NIRSPEC and only three hours on a V = 8 star. <BR /> Conclusions: We conclude that it should thus be possible to distinguish the reference situation of a lava ocean with phase-locking and no atmosphere from other cases. In addition, obtaining the surface temperature map and the albedo brings important constraints on the nature or the physical state of the soil of hot super-Earths.
D. Cébron, M. Le Bars, P. Le Gal, C. Moutou, J. Leconte, and A. Sauret. Elliptical instability in hot Jupiter systems. Icarus, 226:1642-1653, 2013. [ bib | DOI | arXiv | PDF version | ADS link ]
Several studies have already considered the influence of tides on the evolution of systems composed of a star and a close-in companion to tentatively explain different observations such as the spin-up of some stars with hot Jupiters, the radius anomaly of short orbital period planets and the synchronization or quasi-synchronization of the stellar spin in some extreme cases. However, the nature of the mechanism responsible for the tidal dissipation in such systems remains uncertain. In this paper, we claim that the so-called elliptical instability may play a major role in these systems, explaining some systematic features present in the observations. This hydrodynamic instability, arising in rotating flows with elliptical streamlines, is suspected to be present in both planet and star of such systems, which are elliptically deformed by tides. The presence and the influence of the elliptical instability in gaseous bodies, such as stars or hot Jupiters, are most of the time neglected. In this paper, using numerical simulations and theoretical arguments, we consider several features associated to the elliptical instability in hot-Jupiter systems. In particular, the use of ad hoc boundary conditions makes it possible to estimate the amplitude of the elliptical instability in gaseous bodies. We also consider the influence of compressibility on the elliptical instability, and compare the results to the incompressible case. We demonstrate the ability for the elliptical instability to grow in the presence of differential rotation, with a possible synchronized latitude, provided that the tidal deformation and/or the rotation rate of the fluid are large enough. Moreover, the amplitude of the instability for a centrally-condensed mass of fluid is of the same order of magnitude as for an incompressible fluid for a given distance to the threshold of the instability. Finally, we show that the assumption of the elliptical instability being the main tidal dissipation process in eccentric inflated hot Jupiters and misaligned stars is consistent with current data.
E. Bolmont, F. Selsis, S. N. Raymond, J. Leconte, F. Hersant, A.-S. Maurin, and J. Pericaud. Tidal dissipation and eccentricity pumping: Implications for the depth of the secondary eclipse of 55 Cancri e. Astronomy Astrophysics, 556:A17, 2013. [ bib | DOI | arXiv | PDF version | ADS link ]
<BR /> Aims: We use the super Earth 55 Cnc e as a case study to address an observable effect of tidal heating. This transiting short-period planet belongs to a compact multiple system with massive planets. We investigate whether planet-planet interactions can force the eccentricity of this planet to a level affecting the eclipse depth observed with Spitzer. <BR /> Methods: Using the constant time lag tidal model, we first calculate the observed planet flux as a function of albedo and eccentricity, for different tidal dissipation constants and for two extreme cases: a planet with no heat redistribution and a planet with full heat redistribution. We derive the values of albedo and eccentricity that match the observed transit depth. We then perform N-body simulations of the planetary system including tides and general relativity to follow the evolution of the eccentricity of planet e. We compare the range of eccentricities given by the simulations with the eccentricities required to alter the eclipse depth. <BR /> Results: Using our nominal value for the dissipation constant and the most recent estimates of the orbital elements and masses of the 55 Cnc planets, we find that the eccentricity of planet e can be large enough to contribute at a measurable level to the thermal emission measured with Spitzer. This affects the constraints on the albedo of the planet, which can be as high as 0.9 (instead of 0.55 when ignoring tidal heating). We also derive a maximum value for the eccentricity of planet e directly from the eclipse depth: e 0.015 assuming Earth's dissipation constant. <BR /> Conclusions: Transiting exoplanets in multiple planet systems - like 55 Cancri - are exceptional targets for testing tidal models because their tidal luminosity may be observable. Future multi-wavelengths observations of eclipse depth and phase curves (for instance with EChO and JWST) should allow us to better resolve the temperature map of these planets and break the degeneracy between albedo and tidal heating that remains for single band observations. In addition, an accurate determination of the eccentricity will make it possible to constrain the dissipation rate of the planet and to probe its internal structure.
F. Selsis, A.-S. Maurin, F. Hersant, J. Leconte, E. Bolmont, S. N. Raymond, and M. Delbo'. The effect of rotation and tidal heating on the thermal lightcurves of super Mercuries. Astronomy Astrophysics, 555:A51, 2013. [ bib | DOI | arXiv | PDF version | ADS link ]
Short-period (50 day), low-mass ( 10 M⊕) exoplanets are abundant, and the few of them whose radius and mass have been measured already reveal a diversity in composition. Some of these exoplanets are found on eccentric orbits and are subjected to strong tides that affect their rotation and result in significant tidal heating. Within this population, some planets are likely to be depleted in volatiles and have no atmosphere. We modeled the thermal emission of these super Mercuries to study the signatures of rotation and tidal dissipation on their infrared lightcurve. We computed the time-dependent temperature map on the surface and in the subsurface of the planet and the resulting disk-integrated emission spectrum received by a distant observer for any observation geometry. We calculated the illumination of the planetary surface for any Keplerian orbit and rotation. We included the internal tidal heat flow, vertical heat diffusion in the subsurface and generated synthetic lightcurves. We show that the different rotation periods predicted by tidal models (spin-orbit resonances, pseudo-synchronization) produce different photometric signatures, which are observable provided that the thermal inertia of the surface is high, as for solid or melted rocks (but not regolith). Tidal dissipation can also directly affect the lightcurves and make the inference of the rotation more difficult or easier depending on the existence of hot spots on the surface. Infrared lightcurve measurement with the James Webb Space Telescope and EChO can be used to infer exoplanets' rotation periods and dissipation rates and thus to test tidal models. This data will also constrain the nature of the (sub)surface by constraining the thermal inertia.
E. Bolmont, S. N. Raymond, J. Leconte, and S. P. Matt. Effect of the stellar spin history on the tidal evolution of close-in planets. Astronomy Astrophysics, 544:A124, 2012. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. The spin rate of stars evolves substantially during their lifetime, owing to the evolution of their internal structure and to external torques arising from the interaction of stars with their environments and stellar winds. <BR /> Aims: We investigate how the evolution of the stellar spin rate affects, and is affected by, planets in close orbits via star-planet tidal interactions. <BR /> Methods: We used a standard equilibrium tidal model to compute the orbital evolution of single planets orbiting both Sun-like stars and very low-mass stars (0.1 M&sun;). We tested two stellar spin evolution profiles, one with fast initial rotation (1.2 day rotation period) and one with slow initial rotation (8 day period). We tested the effect of varying the stellar and planetary dissipations, and the planet's mass and initial orbital radius. <BR /> Results: For Sun-like stars, the different tidal evolution between initially rapidly and slowly rotating stars is only evident for extremely close-in gas giants orbiting highly dissipative stars. However, for very low-mass stars the effect of the initial rotation of the star on the planet's evolution is apparent for less massive (1 M⊕) planets and typical dissipation values. We also find that planetary evolution can have significant effects on the stellar spin history. In particular, when a planet falls onto the star, it can cause the star to spin up. <BR /> Conclusions: Tidal evolution allows us to differentiate between the early behaviors of extremely close-in planets orbiting either a rapidly rotating star or a slowly rotating star. The early spin-up of the star allows the close-in planets around fast rotators to survive the early evolution. For planets around M-dwarfs, surviving the early evolution means surviving on Gyr timescales, whereas for Sun-like stars the spin-down brings about late mergers of Jupiter planets. In the light of this study, we can say that differentiating one type of spin evolution from another given the present position of planets can be very tricky. Unless we can observe some markers of former evolution, it is nearly impossible to distinguish the two very different spin profiles, let alone intermediate spin-profiles. Nevertheless, some conclusions can still be drawn about statistical distributions of planets around fully convective M-dwarfs. If tidal evolution brings about a merger late in the stellar history, it can also entail a noticeable acceleration of the star at late ages, so that it is possible to have old stars that spin rapidly. This raises the question of how the age of stars can be more tightly constrained.
R. Heller, R. Barnes, and J. Leconte. Habitability of Extrasolar Planets and Tidal Spin Evolution. Origins of Life and Evolution of the Biosphere, 41:539-543, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
Stellar radiation has conservatively been used as the key constraint to planetary habitability. We review here the effects of tides, exerted by the host star on the planet, on the evolution of the planetary spin. Tides initially drive the rotation period and the orientation of the rotation axis into an equilibrium state but do not necessarily lead to synchronous rotation. As tides also circularize the orbit, eventually the rotation period does equal the orbital period and one hemisphere will be permanently irradiated by the star. Furthermore, the rotational axis will become perpendicular to the orbit, i.e. the planetary surface will not experience seasonal variations of the insolation. We illustrate here how tides alter the spins of planets in the traditional habitable zone. As an example, we show that, neglecting perturbations due to other companions, the Super-Earth Gl581d performs two rotations per orbit and that any primordial obliquity has been eroded.
E. Bolmont, S. N. Raymond, and J. Leconte. Tidal evolution of planets around brown dwarfs. Astronomy Astrophysics, 535:A94, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. The tidal evolution of planets orbiting brown dwarfs (BDs) presents an interesting case study because BDs' terrestrial planet forming region is located extremely close-in. In fact, the habitable zones of BDs range from roughly 0.001 to 0.03 AU and for the lowest-mass BDs are located interior to the Roche limit. <BR /> Aims: In contrast with stars, BDs spin up as they age. Thus, the corotation distance moves inward. This has important implications for the tidal evolution of planets around BDs. <BR /> Methods: We used a standard equilibrium tidal model to compute the orbital evolution of a large ensemble of planet-BD systems. We tested the effect of numerous parameters such as the initial semi-major axis and eccentricity, the rotation period of the BD, the masses of both the BD and planet, and the tidal dissipation factors. <BR /> Results: We find that all planets that form at or beyond the corotation distance and with initial eccentricities smaller than ˜0.1 are repelled from the BD. Some planets initially interior to corotation can survive if their inward tidal evolution is slower than the BD's spin evolution, but most initially close-in planets fall onto the BD. <BR /> Conclusions: We find that the most important parameter for the tidal evolution is the initial orbital distance with respect to the corotation distance. Some planets can survive in the habitable zone for Gyr timescales, although in many cases the habitable zone moves inward past the planet's orbit in just tens to hundreds of Myr. Surviving planets can have orbital periods of less than 10 days (as small as 10 h), so they could be observable by transit.
J. Leconte, D. Lai, and G. Chabrier. Distorted, nonspherical transiting planets: impact on the transit depth and on the radius determination. Astronomy Astrophysics, 528:A41, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
In this paper, we quantify the systematic impact of the nonspherical shape of transiting planets caused by tidal forces and rotation on the observed transit depth. Such a departure from sphericity leads to a bias in the derivation of the transit radius from the light curve and affects the comparison with planet structure and evolution models, which assume spherical symmetry. As the tidally deformed planet projects its smallest cross section area during the transit, the measured effective radius is smaller than the one of the unperturbed spherical planet (which is the radius predicted by 1D evolution models). This effect can be corrected by calculating the theoretical shape of the observed planet. Using a variational method and a simple polytropic assumption for the gaseous planet structure, we derived simple analytical expressions for the ellipsoidal shape of a fluid object (star or planet) accounting for both tidal and rotational deformations. We determined the characteristic polytropic indexes that describe the structures of irradiated close-in planets within the mass range 0.3 MJ Mp 75 MJ, at different ages, by comparing polytropic models with the inner density profiles calculated with the full evolution code. Our calculations yield a 20% effect on the transit depth, i.e. a 10% decrease in the measured radius, for the extreme case of a 1 MJ planet orbiting a Sun-like star at 0.01 AU, and the effect can be greater for lower mass objects. For the closest planets detected so far ( 0.05 AU), the effect on the radius is of the order of 1 to 10%, by no means a negligible effect, enhancing the puzzling problem of the anomalously large bloated planets. These corrections must thus be taken into account for correctly determining the radius from the transit light curve and when comparing theoretical models with observations. Our analytical expressions can be easily used to calculate these corrections, caused by the nonspherical shape of the planet, on the observed transit depth and thus to derive the planet's real equilibrium radius, the one to be used when comparing models with observations. They can also be used to model ellipsoidal variations in the stellar flux now detected in the CoRoT and Kepler light curves. We also derive directly usable analytical expressions for the moment of inertia and the Love number (k2) of a fluid planet as a function of its mass and, in the case of significant rotation, for its oblateness.Tables B.2 and B.3 are only available in electronic form at <A href=“http://www.aanda.org”>http://www.aanda.org</A>
R. Heller, J. Leconte, and R. Barnes. Tidal obliquity evolution of potentially habitable planets. Astronomy Astrophysics, 528:A27, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. Stellar insolation has been used as the main constraint on a planet's potential habitability. However, as more Earth-like planets are discovered around low-mass stars (LMSs), a re-examination of the role of tides on the habitability of exoplanets has begun. Those studies have yet to consider the misalignment between a planet's rotational axis and the orbital plane normal, i.e. the planetary obliquity. <BR /> Aims: This paper considers the constraints on habitability arising from tidal processes due to the planet's spin orientation and rate. Since tidal processes are far from being understood we seek to understand differences between commonly used tidal models. <BR /> Methods: We apply two equilibrium tide theories - a constant-phase-lag model and a constant-time-lag model - to compute the obliquity evolution of terrestrial planets orbiting in the habitable zones around LMSs. The time for the obliquity to decrease from an Earth-like obliquity of 23.5deg to 5deg, the “tilt erosion time”, is compared to the traditional insolation habitable zone (IHZ) in the parameter space spanned by the semi-major axis a, the eccentricity e, and the stellar mass Ms. We also compute tidal heating and equilibrium rotation caused by obliquity tides as further constraints on habitability. The Super-Earth Gl581 d and the planet candidate Gl581 g are studied as examples for these tidal processes. <BR /> Results: Earth-like obliquities of terrestrial planets in the IHZ around stars with masses 0.25 M&sun; are eroded in less than 0.1 Gyr. Only terrestrial planets orbiting stars with masses 0.9 M&sun; experience tilt erosion times larger than 1 Gyr throughout the IHZ. Tilt erosion times for terrestrial planets in highly eccentric orbits inside the IHZ of solar-like stars can be 10 Gyr. Terrestrial planets in the IHZ of stars with masses 0.25 M&sun; undergo significant tidal heating due to obliquity tides, whereas in the IHZ of stars with masses 0.5 M&sun; they require additional sources of heat to drive tectonic activity. The predictions of the two tidal models diverge significantly for e 0.3. In our two-body simulations, Gl581 d's obliquity is eroded to 0deg and its rotation period reached its equilibrium state of half its orbital period in 0.1 Gyr. Tidal surface heating on the putative Gl581 g is 150 mW/m2 as long as its eccentricity is smaller than 0.3. <BR /> Conclusions: Obliquity tides modify the concept of the habitable zone. Tilt erosion of terrestrial planets orbiting LMSs should be included by atmospheric modelers. Tidal heating needs to be considered by geologists.
J. Leconte, G. Chabrier, I. Baraffe, and B. Levrard. Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity. Astronomy Astrophysics, 516:A64, 2010. [ bib | DOI | arXiv | PDF version | ADS link ]
We present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut (1981) model, valid at any order in eccentricity, obliquity and spin. We demonstrate both analytically and numerically that except if the system was formed with a nearly circular orbit (e 0.2), consistently solving the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at 2nd order in eccentricity, as done in all previous studies, lead to quantitatively and sometimes even qualitatively erroneous tidal evolutions. As a consequence, tidal energy dissipation rates are severely underestimated in all these calculations and the characteristic timescales for the various orbital parameters evolutions can be wrong by up to three orders of magnitude. These discrepancies can by no means be justified by invoking the uncertainty in the tidal quality factors. Based on these complete, consistent calculations, we revisit the viability of the tidal heating hypothesis to explain the anomalously large radius of transiting giant planets. We show that even though tidal dissipation does provide a substantial contribution to the planet's heat budget and can explain some of the moderately bloated hot-Jupiters, this mechanism can not explain alone the properties of the most inflated objects, including HD 209 458 b. Indeed, solving the complete tidal equations shows that enhanced tidal dissipation and thus orbit circularization occur too early during the planet's evolution to provide enough extra energy at the present epoch. In that case either a third, so far undetected, low-mass companion must be present to keep exciting the eccentricity of the giant planet, or other mechanisms - stellar irradiation induced surface winds dissipating in the planet's tidal bulges and thus reaching the convective layers, inefficient flux transport by convection in the planet's interior - must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.
J. Leconte, I. Baraffe, G. Chabrier, T. Barman, and B. Levrard. Structure and evolution of the first CoRoT exoplanets: probing the brown dwarf/planet overlapping mass regime. Astronomy Astrophysics, 506:385-389, 2009. [ bib | DOI | arXiv | PDF version | ADS link ]
We present detailed structure and evolution calculations for the first transiting extrasolar planets discovered by the space-based CoRoT mission. Comparisons between theoretical and observed radii provide information on the internal composition of the CoRoT objects. We distinguish three different categories of planets emerging from these discoveries and from previous ground-based surveys: (i) planets explained by standard planetary models including irradiation; (ii) abnormally bloated planets; and (iii) massive objects belonging to the overlapping mass regime between planets and brown dwarfs. For the second category, we show that tidal heating can explain the relevant CoRoT objects, providing non-zero eccentricities. We stress that the usual assumption of a quick circularization of the orbit by tides, as usually done in transit light curve analysis, is not justified a priori, as suggested recently by Levrard et al. (2009), and that eccentricity analysis should be carefully redone for some observations. Finally, special attention is devoted to CoRoT-3b and to the identification of its very nature: giant planet or brown dwarf? The radius determination of this object confirms the theoretical mass-radius predictions for gaseous bodies in the substellar regime but, given the present observational uncertainties, does not allow an unambiguous identification of its very nature. This opens the avenue, however, to an observational identification of these two distinct astrophysical populations, brown dwarfs and giant planets, in their overlapping mass range, as done for the case of the 8 Jupiter-mass object Hat-P-2b. According to the presently published error bars for the radius determination and to our present theoretical description of planet structure and evolution, the high mean density of this object requires a substantial metal enrichment of the interior and is inconsistent at about the 2-sigma limit with the expected radius of a solar-metallicity brown dwarf. Within the aforementioned observational and theoretical determinations, this allows a clear identification of its planetary nature, suggesting that planets may form up to at least 8 Jupiter masses.